Narrow Results

This paper presents two classes of integer codes called integer SEC-(DAED)${}_b$ codes and integer SEC-DAED codes. The first class of codes can correct all single errors and detect all double adjacent (DA) errors within a $b$-bit byte, while the second class of codes has the ability to correct all single errors and detect all DA errors. Both classes of codes are defined over integer rings and are generated by computer search. To evaluate the performance of the proposed codes, we analyze the probability of incorrect decoding for different error rates. In addition, the paper shows that the proposed codes have a slightly higher redundancy than linear SEC-DAED codes, but also a much simpler decoding algorithm.

We consider the problem of evaluating a boolean function P(x₁,…,x_n), by asking queries of the form “x_i=?”, and receiving answers which may not always be truthful. Assuming that the total number of lies does not exceed E, we present an algorithm with cost O(n+s_PE+t_PE), where s_P is the maximal size of a minterm of P(x) and t_P ‘is the maximal size of a maxterm. We also prove that if P is monotone, then any algorithm for evaluating P must ask Ω(s_PE+t_PE) queries for some input.

In recent years, intense usage of computing has been the main strategy of investigations in several scientific research projects. The progress in computing technology has opened unprecedented opportunities for systematic collection of experimental data and the associated analysis that were considered impossible only few years ago.

This paper focuses on the strategies in use: it reviews the various components that are necessary for an effective solution that ensures the storage, the long term preservation, and the worldwide distribution of large quantities of data that are necessary in a large scientific research project.

The paper also mentions several examples of data management solutions used in High Energy Physics for the CERN Large Hadron Collider (LHC) experiments in Geneva, Switzerland which generate more than 30,000 terabytes of data every year that need to be preserved, analyzed, and made available to a community of several tenth of thousands scientists worldwide.

We used Engle–Granger cointegration test to investigate and compare the long-run performance of imports and exports in Pakistan, India, Sri Lanka, Korea and Thailand. Graphical analysis demonstrates an inherent tendency of imports and exports to move together in the long run. Cointegration and error correction results support the graphical analysis that these countries do not violate on the average the international budget constraint, and trade disequilibrium is a short-run phenomenon that is sustainable in the long run. Macroeconomic policies in the sample countries have been adequately effective to affect long-run equilibrium between imports and exports. The international events had differential impact on each country of our sample.

Examining the impact of remittances on private investment, the study finds that remittances have an adverse impact on private investment and hence is apprehensive about its net positive impact on output growth in India. Therefore, the study suggests that the government policy should be designed toward inducing private sector to allocate more remittances for investments for leveling up the rate of economic growth. Otherwise, a significant proportion of remittances would result in increase in private consumption without desired contributory impact. The study also observes crowding out impact of public sector investment, while openness measure raises private sector investment.

Grid adaptation is an important strategy to improve the accuracy of output functions (e.g. drag, lift, etc.) in computational fluid dynamics (CFD) analysis and design applications. This paper presents a modified robust grid adaptation and error correction method for reducing simulation errors in integral outputs. The procedure is based on discrete adjoint optimization theory in which the estimated global error of output functions can be directly related to the local residual error. According to this relationship, local residual error contribution can be used as an indicator in a grid adaptation strategy designed to generate refined grids for accurately estimating the output functions. This grid adaptation and error correction method is applied to subsonic and supersonic simulations around three-dimensional configurations. Numerical results demonstrate that the sensitive grids to output functions are detected and refined after grid adaptation, and the accuracy of output functions is obviously improved after error correction. The proposed grid adaptation and error correction method is shown to compare very favorably in terms of output accuracy and computational efficiency relative to the traditional featured-based grid adaptation.

In this paper we present a fast algorithm for the computation of error-correcting graph isomorphisms. The new algorithm is an extension of a method for exact subgraph isomorphism detection from an input graph to a set of a priori known model graphs, which was previously developed by the authors. Similar to the original algorithm, the new method is based on the idea of creating a decision tree from the model graphs. This decision tree is compiled off-line in a preprocessing step. At run time, it is used to find all error-correcting graph isomorphisms from an input graph to any of the model graphs up to a certain degree of distortion. The main advantage of the new algorithm is that error-correcting graph isomorphism detection is guaranteed to require time that is only polynomial in terms of the size of the input graph. Furthermore, the time complexity is completely independent of the number of model graphs and the number of edges in each model graph. However, the size of the decision tree is exponential in the size of the model graphs and the degree of error. Nevertheless, practical experiments have indicated that the method can be applied to graphs containing up to 16 vertices.

This paper presents a class of integer codes suitable for use in optical networks with low error rates. The presented codes are constructed with the help of a computer and have two important features: first, they can correct single errors affecting one or two $b$-bit bytes, and second, they use processor-friendly operations to encode/decode data bits. The effectiveness of the presented codes is demonstrated on theoretical models of four-core and six-core processors. The obtained results show that the decoder throughput reaches 14.70Gbps, which is above the operating speed of 10G networks. Finally, the paper compares the proposed codes with BCH codes of similar properties. The comparison is made in terms of redundancy and the number of decoding operations.

As the feature sizes of integrated circuits are reduced to the nanometer scale, the total soft error rate (SER) in memory and the proportion of multiple bit upsets (MBUs) are significantly increasing. In order to ensure the information reliability, many error correction codes with strong error correction ability were proposed, such as Reed–Somolon (RS) code and Bose–Chaudhuri–Hocquenghem (BCH) code. However, these error correction codes have limited error correction capability, high algorithm complexity and large data redundancy. In this paper, a novel fault tolerance method for locating and correcting multiple bit errors in memory is proposed based on data similarity. The proposed method uses the inner product as the metric to analyze the similarity of the pre-protected data from the vertical and horizontal dimensions, respectively, and to construct the model of error location and correction. This method performs encoding and decoding in units of blocks and detecting and correcting in units of words, so it can correct any number of bits in a corrupted word with low redundancy overhead. Finally, irradiation tests were conducted on a commercial SRAM, and the feasibility of the proposed method is verified by using heavy ion ${}^{86}$Kr${}^{26+}$ as irradiation source.

Soft errors are the most common aspect of errors that are incurred in the memory devices during transmission. The common and fundamental reason of these soft errors is radiation that produces leakage of current and results in misleading information which is sent to various transmission stations via satellite and microwave communication. In this paper, the real-time embedded system is designed and implemented to mitigate the soft error using hybrid Hamming code. The work also develops the hardware system for soft error mitigation. The designed system is compared with the other coding schemes that are commonly available for error mitigation. The performance of real-time embedded system for soft error mitigation is carried out using signal-to-noise ratio and other performance metrics. The timing diagram analysis is the key metrics of the paper that defined the performance of the designed soft error mitigation design using the proposed technique. Furthermore, the results of the designed systems are demonstrated using bit error probability, Pb and channel symbol error probability (CSEP). The impact of the designed system will be that from now onwards using the proposed system, the soft error produced due to radiation and other reasons would not affect too much on transmission and reception of important data via satellite and microwave communication.

A Rao–Nam cryptosystem based on error correction code is proposed to provide both security and reliability. Since its security is drastically constrained by the limited error syndromes, in this paper, an improved Rao–Nam cryptosystem based on fractional order hyperchaotic system and Extended Difference Family–Quasi-Cyclic–Low-Density Parity-Check (EDF–QC–LDPC) codes is proposed to improve the security. A four-dimensional fractional order hyperchaotic system is constructed and is used to generate an excellent pseudorandom sequence. By replacing error syndromes with the pseudorandom sequence and permuting the coded message dynamically, the security of the Rao–Nam cryptosystem is enhanced greatly. The ability of the improved Rao–Nam cryptosystem against known attacks is analyzed and the error correction performance with different parameters is simulated. The results show that the proposed cryptosystem has a significant advantage of resisting the chosen-plaintext attack. Moreover, the proposed cryptosystem retains high capacity of error correction.

We propose an abductive model based on Constraint Handling Rule Grammars (CHRGs) for detecting and correcting errors in problem domains that can be described in terms of strings of words accepted by a logic grammar. We provide a proof of concept for the specific problem of detecting and repairing natural language errors, in particular, those concerning feature agreement. Our methodology relies on grammar and string transformation in accordance with a user-defined dictionary of possible repairs. This transformation also serves as top-down guidance for our essentially bottom-up parser. With respect to previous approaches to error detection and repair, including those that also use constraints and/or abduction, our methodology is surprisingly simple while far-reaching and efficient.

For predicting missile’s interception point, the current guidance law based on neural networks avoids to model the strong nonlinear motion of a missile and simultaneously improve the anti-jamming ability of the guidance law. Although the advantages of solving the predicted intercept point problem based on neural networks are obvious, the difficulty in obtaining the target missile information still exists. In this work, we propose a dead-reckoning navigation guidance (DRNG) law. First, a neural network-based collaborative forecast scheme is proposed and utilize the advantages of different neural networks to greatly reduce the difficulty in acquiring the target information. Second, we construct an approximate realistic aerodynamic characteristics environment to simulate the motion parameters of missiles and targets. We also introduce real-time error correction for increasing the prediction accuracy of the network and improve the robustness of the proposed DRNG by using the model self-update algorithm. Finally, through a large number of simulation experiments, results show that the proposed DRNG completes the interception task in a noisy environment, when only the position parameters of a target missile are known. Moreover, it has a more optimized ballistic trajectory as compared with the traditional guidance law.

It is argued that the existing schemes of fault-tolerant quantum computation, designed for discrete time models and based on quantum error correction, fail for continuous time Hamiltonian models, even with Markovian noise.

We introduce an information theoretic framework for a quantitative measure of originality to model the impact of various classes of biases, errors and error corrections on scientific research. Some of the open problems are also outlined.

The possibility of building a quantum computer is critically analyzed. The main point is that the general state of the hypothetical quantum computer with N qubits is characterized by 2^N quantum amplitudes, which are complex numbers restricted by the normalization condition only. It looks highly improbable that it will ever be possible to keep under our control this number of complex parameters even for modest values of $N\sim$ 50 or 100.

Utilizing a partially entangled GHZ state, we propose a novel controlled quantum secure direct communication (QSDC) with quantum encryption. Under the supervision and help of the third side, the sender and the receiver can securely share the private quantum entanglement keys used to encrypt and decrypt the secret message. According to the results of checking the eavesdropping on decoy photons, communicators can decide whether the quantum keys are reused in the next round. Not only will eavesdropping inevitably disturb the states of the decoy photons and be detected, but arbitrary transmission errors can also be corrected.

We consider the series of Fibonacci n-step numbers and a class of square matrix of order n based on Fibonacci n-step numbers with determinant +1 or -1. Thereby, we introduce a new coding theory called Fibonacci n-step coding theory and establish generalized relation among the code elements for all values of n. For n = 2, the correct ability of the method is 93.33%; for n = 3, the correct ability of the method is 99.80% and for n = 4, the correct ability of the method is 99.998%. In general, the correct ability of the method increases as n increases.

Motivated from the theory of quantum error correcting codes, we investigate a combinatorial problem that involves a symmetric n-vertices colorable graph and a group of operations (coloring rules) on the graph: find the minimum sequence of operations that maps between two given graph colorings. We provide an explicit algorithm for computing the solution of our problem, which in turn is directly related to computing the distance (performance) of an underlying quantum error correcting code. Computing the distance of a quantum code is a highly non-trivial problem and our method may be of use in the construction of better codes.

We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and correction algorithms of golden cryptography previously known only for recurrences of a special form. They are based on proving the checking relations (inequalities satisfied by the ciphertext) under the condition that the analog of the golden Q-matrix has the strong Perron–Frobenius property. These algorithms are proved to be especially efficient when the characteristic polynomial of the recurrence is a Pisot polynomial. Finally, we outline algorithms for generating recurrences that satisfy our conditions.